Central limit theorems for weighted sums of exchangeable random elements in banach spaces(1)

1984 ◽  
Vol 2 (3) ◽  
pp. 229-244
Author(s):  
Peter Z. Daffer
Keyword(s):  
Banach Spaces ◽  
Central Limit ◽  
Limit Theorems ◽  
Central Limit Theorems ◽  
Weighted Sums ◽  
Random Elements

CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES: LP -APPROXIMABILITY VERSUS BROWNIAN MOTION

2009 ◽  
Vol 25 (3) ◽  
pp. 748-763 ◽  
Author(s):  
Kairat T. Mynbaev
Keyword(s):  
Brownian Motion ◽  
Central Limit ◽  
Asymptotic Expansions ◽  
Limit Theorems ◽  
Stochastic Calculus ◽  
Central Limit Theorems ◽  
Weighted Sums ◽  
Linear Processes

Standardized slowly varying regressors are shown to be Lp-approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

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